Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 749 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.If a − b = 3 and ab = 108, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 65².
3. 3.Use (a − b)² = a² − 2ab + b² to find 21².
4. 4.If a + b = 12 and ab = 27, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 98² − 87².
6. 6.Use (a − b)² = a² − 2ab + b² to find 49².
7. 7.Use (a − b)² = a² − 2ab + b² to find 46².
8. 8.Use a² − b² = (a + b)(a − b) to find 55² − 13².
9. 9.Use (a + b)² = a² + 2ab + b² to find 91².
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Find the value of x² − 2xy + y² when x = 12 and y = 7.
12. 12.If a + b = 10 and ab = 21, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 47² − 19².
14. 14.Use a² − b² = (a + b)(a − b) to find 37² − 27².
15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 1.
16. 16.Use (a + b)² = a² + 2ab + b² to find 36².
17. 17.Use (a + b)² = a² + 2ab + b² to find 62².
18. 18.Use (a + b)(a − b) = a² − b² to find 74 × 66.
19. 19.Use a² − b² = (a + b)(a − b) to find 24² − 13².
20. 20.Find the value of x² + 2xy + y² when x = 15 and y = 4.
21. 21.Use (a + b)(a − b) = a² − b² to find 21 × 19.
22. 22.Use (a + b)(a − b) = a² − b² to find 26 × 14.
23. 23.Use (a + b)² = a² + 2ab + b² to find 45².
24. 24.If a + b = 5 and ab = 6, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 13 and y = 9.
26. 26.Use (a + b)(a − b) = a² − b² to find 67 × 53.
27. 27.Find the value of x² − 2xy + y² when x = 11 and y = 1.
28. 28.Use (a − b)² = a² − 2ab + b² to find 39².
29. 29.Find the value of x² − y² when x = 11 and y = 3.
30. 30.If a − b = 1 and ab = 42, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 75 × 65.
32. 32.Find the value of x² − y² when x = 4 and y = 2.
33. 33.Use (a + b)² = a² + 2ab + b² to find 107².
34. 34.Use (a + b)² = a² + 2ab + b² to find 43².
35. 35.Find the value of x² − y² when x = 14 and y = 5.
36. 36.Find the value of x² − 2xy + y² when x = 8 and y = 3.
37. 37.Use (a + b)² = a² + 2ab + b² to find 74².
38. 38.Use (a + b)² = a² + 2ab + b² to find 102².
39. 39.Use (a + b)² = a² + 2ab + b² to find 15².
40. 40.Find the value of x² + 2xy + y² when x = 14 and y = 2.

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